"To support this view, he added a second argument that there are no unproductive types of labor under capitalism, because all labor employed by capital at a profit produces surplus-value."
I most certainly did not. I said that public sector and finance sector workers are not productive labour, but that not all business service workers could be dismissed as 'unproductive'. I wrote in my email of 18 November
"I think Marx is right that the financial services do not increase surplus value, but only lay claim to value that has been created elsewhere."
and also that
"Also the massive expansion of public sector employment, while it is good for recipents of NHS care, is obviously not boosting British profits."
And I did add that
"Plainly the 400 million additional workers world wide are not in financial intermediation or working for the NHS."